How To Do Long Division With Decimals

This video features a teacher giving a summary of long division with decimals. He explains everything he does in simple English with all the mathematical terms such as long division and decimals.

Hi, my name is Charles and I am one of the Mathematics teachers from the Maxim workshop. I am just going to, now, teach you how to do some mathematics! I am going to show you how to do long division with decimal numbers. Now, division and decimal numbers are by themselves tricky topics, but I am going to try to bring together an easy way to deal with both of them at the same time.

The first thing we will do is write out our sum and what we are going to do here is, we have 72.4 divided by 1.1.

Now this is a simple division that we are going to do, just to show you the techniques that we are going to use. Now, what we are trying to do on the denominator is remove the decimal point. So what we are going to do is bring the decimal point back here, and then however many times it takes us to remove the decimal point from just the denominator, that's how many times we move the denominator back on the top numerator.

So, this is the equivalent of multiplying by ten, this is the equivalent of multiplying by ten also. Now, you have not changed the fraction, in terms of its weight, but you have changed the actual numbers in the fraction, so you have just basically changed the equivalent fraction. So, the first thing we are going to do is rub this out, rub that out; 72.

4 times 10 equals 724; divided by 1.1 times 10, and that equals 11. So, you've converted your normal decimal fraction into an equivalent fraction that has no decimals.

And then you can progress with your normal long division. So, we have to do our tableau again, so we have got 724 divided by 11. So, the first thing we need to do is to establish how many times 11 goes into 7, and it does not, so we put a 0 above there.

Now this number needs to be multiplied by 11 to go below here, so it would just give us zero, so we do not really need to worry about that. So now, we need to see how many times 11 goes into 72. So 11 goes into 72 six times to give you 66 and then we have a remainder of 4 and 2, so that's just 6 again.

So, it goes as 6 times. Six times 11 gives us 66. Now we do 72 again, and take away 66; that will give us 6.

Now, we bring the 4 down here to give us 64. Now we have to think about how many times 11 goes into 64. Now, if you remember when we multiplied 11 by 6 it gave us 66, so that's above 64, so it tells us that 11 can only end to 64 five times, giving us 55.

So we write the 5 here and then we multiply this 5 by 11 which again gives us 55 which we were looking for, and then we say 64, take away 55, now that gives us 9. Now, this 9 is our remainder, so what we are looking to do now is set it up like this. The whole number on the top goes here - 65 - and we have 9, which is our remainder, here, and we still want to divide the remainder by 11, so we will not put 65, remainder 9, because that 9 still needs to be divided by the 11, so we'll put 65 and 9, as a remainder, divided by 11.

Commonly, in schools, they will teach you this, but if you think about if there were 724 cakes, and there were 11 of you and your friends, you would probably share all of the cakes, you will not just leave a remainder of 9. So that is the way you have to think of what is happening there. And your answer is pretty much 65 and 9 elevenths.